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A cross-monotonic cost sharing method for the facility location game with service installation costs

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Abstract

In this paper, we consider the metric uncapacitated facility location game with service installation costs. Our main result is an 11-approximate cross-monotonic cost-sharing method under the assumption that the installation cost depends only on the service type.

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References

  1. Shmoys D, Tardos É, Aardal K. Approximation algorithms for facility location problems (extended abstract). In: Proceedings of the 29th ACM Symposium on Theory of Computing (STOC). New York: ACM, 1997, 265–274

    Google Scholar 

  2. Byrka J, Aardal K. An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem. SIAM J Comput, to appear (2009)

  3. Chudak F, Shmoys D. Improved approxiamtion algorithms for the uncapaciteted facility location problem. SIAM J Comput, 33(1): 1–25 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Guha S, Khuller S. Greedy strike back: Improved facility location algorithms. J Algorithms, 31: 228–248 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Jain K, Mahdian M, Saberi A. A new greedy approach for facility location problems. In: Proceedings of the 34th ACM Symposium on Theory of Computing (STOC). New York: ACM, 2002, 731–740

    Google Scholar 

  6. Jain K, Vazirani V V. Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation. J ACM, 48: 274–296 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Mahdian M, Ye Y, Zhang J. Approximation algorithms for metric facility location problems. SIAM J Comput, 36(2): 411–432 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Sviridenko M. An improved approximation algorithm for the metric uncapacitated facility location problem. In: Proceedings of the 9th Integer Programming and Combinatorial Optimization (IPCO). Berlin-Heidelberg: Springer, 2002, 240–257

    Google Scholar 

  9. Aardal K, Chudak F, Shmoys D. A 3-approximation algorithm for the k-level uncapacitated facility location problem. Inform Process Lett, 72: 161–167 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ageev A, Ye Y, Zhang J. Improved combinatorial apporximation algorithms for the k-level facility location problem. SIAM J Discrete Math, 18(1): 207–217 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Du D, Wang X, Xu D. An approximation algorithm for the k-level capacitated facility location problem. J Comb Optim, DOI: 10.1007/s10878-009-9213-1

  12. Shmoys D, Swamy C, Levi R. Facility location with service installation costs. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Philadelphia: SIAM, 2004, 1088–1097

    Google Scholar 

  13. Xu D, Du D. The k-level facility location game. Oper Res Lett, 34(4): 421–426 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Xu D, Yang R. A cost-sharing method for an economic lot-sizing game. Oper Res Lett, 37: 107–110 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhang J. Approximating the two-level facility location problem via a quasi-greedy approach. Math Program Ser A, 108(1): 159–176 (2006)

    Article  MATH  Google Scholar 

  16. Zhang J, Chen B, Ye Y. A multiexchange local search algorithm for the capacitated facility location problem. Math Oper Res, 30(2): 389–403 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  17. Zhang J, Ye Y. A note on the maximization version of the multi-level facility location problem. Oper Res Lett, 30(5): 333–335 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  18. Xu D, Zhang S. Approximation algorithm for facility location with service installation costs. Oper Res Lett, 6: 46–50 (2008)

    Article  Google Scholar 

  19. Moulin H, Shenker S. Strategyproof sharing of submodular costs: budget balance versus efficiency. Econom Theory, 18: 511–533 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  20. Pál M, Tardos É. Group strategyproof mechanisms via primal-dual algorithms. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS). Washington: IEEE 2003, 584–593

    Chapter  Google Scholar 

  21. Immorlica N, Mahdian M, Mirrokni V S. Limitations of cross-monotonic cost sharing schemes. In: Proceedings of the 16th Annual ACM-SIAM symposium on Discrete algorithms (SODA). New York: ACM, 2005, 602–611

    Google Scholar 

  22. Goemans M X, Skutella M. Cooperative facility location games. J Algorithms, 50: 194–214 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  23. Mallozzi L. Noncooperative facility location games. Oper Res Lett, 35(2): 151–154 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  24. Leonardi S, Schäfer G. Cross-monotonic cost sharing methods for connected facility location games. Theoret Comput Sci, 326: 431–442 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  25. Li Y, Xu D. Soft-capacitated facility location game. Acta Math Appl Sin Engl Ser, DOI: 10.1007/S10255-008-8111-0

  26. Devanur N R, Mihail M, Vazirani V V. Strategyproof cost-sharing mechanisms for set cover and facility location games. Decis Supp Syst, 39: 11–22 (2005)

    Article  Google Scholar 

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Correspondence to DaChuan Xu.

Additional information

This work was supported by National Natural Science Foundation of China (Grant Nos. 60773185, 10401038) and Program for Beijing Excellent Talents (Grant No. 20071D050150020S)

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Xu, D. A cross-monotonic cost sharing method for the facility location game with service installation costs. Sci. China Ser. A-Math. 52, 2530–2536 (2009). https://doi.org/10.1007/s11425-009-0173-9

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  • DOI: https://doi.org/10.1007/s11425-009-0173-9

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